reactive power and harmonic compensation: a case study for ... · cifically for high power...

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Reactive power and harmonic compensation: A case study for the coal-mining industry

F. Roos1, R.C. Bansal2*

1 Department of Electrical, Electronics and Computer Engineering, University of Pretoria, Hatfield Campus, Pretoria 0028, South Africa

2 Electrical and Computer Engineering Department, University of Sharjah, Sharjah, P.O. Box 27272, United Arab Emirates

Abstract This study reports on a case study in Grootegeluk Mine: Exxaro Coal, Lephalale, South Africa, in terms of power factor correction (PFC), load flow, harmonic frequency scans and harmonic voltage distortion anal-yses. The DIgSilent PowerFactory software was used for network simulations. Harmonic and reactive power compensation techniques were compared in terms of filter type evolution and technology advancement, with the use of simple trade-off criteria such as cost-effectiveness versus performance. It was found that both pas-sive and hybrid filters were more favourable and could effectively compensate all voltage and current har-monics and reactive power for large nonlinear loads. The installation of switched PFC filter banks tuned at the fifth harmonic order accommodates future network growth and this solution can be rolled out to any mining industry as a benchmark to lower energy cost and maximise savings achievable on the electricity bill.

Keywords: electrical energy, passive filter, reactive power compensation, total harmonic distortion

Journal of Energy in Southern Africa 30(1): 34-48 DOI: http://dx.doi.org/10.17159/2413-3051/2019/v30i1a2473

Published by the Energy Research Centre, University of Cape Town ISSN: 2413-3051 http://journals.assaf.org.za/jesa

Sponsored by the Department of Science and Technology

Corresponding author: Tel: +971 6 5050971; email: [email protected]

Volume 30 Number 1

35 Journal of Energy in Southern Africa • Vol 30 No 1 • February 2019

1. Introduction All areas of industry need to cut production ex-penses because of tough economic conditions. Low-ering the cost of energy by means of power quality improvement is crucial to assist in business sustain-ability. Presently power quality is dirty and compro-mised because of harmonic producing inductive loads [1–3]. Harmonic propagation is caused by an increase in the use of variable speed drives amongst other power electronics in industry, driven by energy saving initiatives [4]. Nonlinear loads typically have low input power factors (PFs), while sourcing sub-stantial harmonic currents, which create severe is-sues at the power supply system [1]. Passive filters, i.e., resonant circuit (LC) filters, have been used tra-ditionally to get rid of current harmonics of the retic-ulation network. System PF was improved by using capacitors to compensate inductive alternating cur-rent loads. A major drawback found in using this type of filter is that it suffers from resonance [1–3]. Reactive power and harmonic compensation have been realised by means of thyristor-switched filters (TSFs) containing numerous passive filter collections installed in the networks [2]. The amount of TSF’s compensation is adjusted in accordance with load power fluctuations [3]. A drawback found in using this type of filter is that resonance could also occur between impedance of the grid and the TSF. The problems related to resonance highlighted in passive filters have been mitigated in the development of ac-tive filters to bring about more dynamic and adjust-able solutions by making use of power electronics [4–6]. Active filters have shown better performance and effectiveness in harmonic compensation [7, 8]. High cost for active filters is a drawback in terms of economic viability and high-power converter ratings are also required [9]. Hybrid filters effectively miti-gate the problems and drawbacks of pure passive filter and/or pure active filter solutions. Hybrid filters provide cost-effective harmonic compensation, spe-cifically for high power nonlinear loads, [10–13]. Numerous hybrid filter topology variations have been reported in the literature [14, 15]. One of the most popular methods identified is a combination of a shunt hybrid power filter (SHPF) and a thyristor-controlled reactor (TCR). This SHPF-TCR hybrid PF corrector effectively eliminates the current harmon-ics and compensates the reactive power sourced from the load [1, 2]. However, both passive and hy-brid technologies are feasible and economically via-ble solutions.

In this study, various PFC methodologies suita-ble for the specific plant environment at Grootegeluk Mine: Exxaro Coal were investigated. A technical so-lution was proposed to maximise savings achievable on the Eskom (national power utility) electricity bill. The objective was to effectively eliminate the har-monics and compensate reactive power subject to

various constraints. The resulting PF and % total harmonic distortion (THD) had to be within the pre-scribed limits [8]. This research focused on finding the most optimal reactive power compensation strat-egy for the typical harsh mining environments gov-erned by the Mine Health and Safety Act. A com-pensation strategy would be designed (a trade-off based on voltage, harmonic effects, type of filter and control philosophy), which would incorporate the design criteria related to mining operations. The overall PF was anticipated to improve to above 0.96 and the % THD to be within acceptable limits, which was of prime importance to lower the energy costs and prevent equipment damage, respectively. The proposed technical solution would maximise the electricity savings.

2. Background overview 2.1 Definition of power factor and total harmonic distortion The PF provides a measure of the effective utilisa-tion of real power (P) in the network. It also denotes the relation between the line voltage and line current and corresponding phase angle between them [16]. The PF is defined in literature as Equation 1 [17, 18].

𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑃𝑃𝑃𝑃 (𝑃𝑃𝑃𝑃) = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑝𝑝𝑝𝑝𝑝𝑝𝑅𝑅𝑝𝑝 (𝑃𝑃)𝐴𝐴𝑝𝑝𝑝𝑝𝑅𝑅𝑝𝑝𝑅𝑅𝑛𝑛𝑛𝑛 𝑝𝑝𝑝𝑝𝑝𝑝𝑅𝑅𝑝𝑝 (𝑆𝑆)

(1)

Equation (1) then takes the form of Equation 2

𝑃𝑃𝑃𝑃 = 𝐼𝐼𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑉𝑉𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠 cos𝜃𝜃𝐼𝐼𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑉𝑉𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠

= cos 𝜃𝜃 (2)

where Is,rms and Vs,rms are root mean square (rms) val-ues of line current and line voltage, respectively and 𝜃𝜃 is phase angle between the respective phase current and phase voltage.

The 𝜃𝜃 is valid only for linear systems. In a system where electronic equipment is installed like active power switching devices, a non-linear behaviour will be experienced, therefore, rendering Equation 2 in-valid [16]. Line voltage and line current become dis-torted because of the nonlinear load. Equations 3 and 4 give the Fourier expansion representations for the line current and line voltage, respectively [16–18].

𝐼𝐼𝑠𝑠(𝑓𝑓) = 𝐼𝐼𝐷𝐷𝐷𝐷 + ∑ 𝐼𝐼𝑠𝑠𝑛𝑛 sin(𝑛𝑛𝑛𝑛𝑓𝑓 + 𝜃𝜃𝑖𝑖𝑛𝑛) = 𝐼𝐼𝐷𝐷𝐷𝐷 +∞𝑛𝑛=1

𝐼𝐼𝑠𝑠1 sin(𝑛𝑛𝑓𝑓 + 𝜃𝜃𝑖𝑖1) + ∑ 𝐼𝐼𝑠𝑠𝑛𝑛 sin(𝑛𝑛𝑛𝑛𝑓𝑓 + 𝜃𝜃𝑖𝑖𝑛𝑛)∞𝑛𝑛=2 (3)

𝑉𝑉𝑠𝑠(𝑓𝑓) = 𝑉𝑉𝐷𝐷𝐷𝐷 + ∑ 𝑉𝑉𝑠𝑠𝑛𝑛 sin(𝑛𝑛𝑛𝑛𝑓𝑓 + 𝜃𝜃𝑣𝑣𝑛𝑛) = 𝑉𝑉𝐷𝐷𝐷𝐷 +∞𝑛𝑛=1

𝑉𝑉𝑠𝑠1 sin(𝑛𝑛𝑓𝑓 + 𝜃𝜃𝑣𝑣1) + ∑ 𝑉𝑉𝑠𝑠𝑛𝑛 sin(𝑛𝑛𝑛𝑛𝑓𝑓 + 𝜃𝜃𝑣𝑣𝑛𝑛)∞𝑛𝑛=2 (4)

Using Equation 1 as reference, PF can now be ex-pressed as in Equation 5.


𝑃𝑃𝑃𝑃 = ∑ 𝐼𝐼𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑉𝑉𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑐𝑐𝑝𝑝𝑠𝑠𝜃𝜃𝑠𝑠∞𝑠𝑠=1

𝐼𝐼𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑉𝑉𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠=

∑ 𝐼𝐼𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑉𝑉𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠𝑐𝑐𝑝𝑝𝑠𝑠𝜃𝜃𝑠𝑠∞𝑠𝑠=1

�∑ (𝐼𝐼𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠)2 ∑ (𝑉𝑉𝑠𝑠𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠)2∞𝑠𝑠=1

∞𝑠𝑠=1

(5)

where Vsn,rms and Isn,rms are rms values of the nth har-monic voltage and line current, respectively and 𝜃𝜃𝑛𝑛 is the phase angle between the respective phase cur-rent and phase voltage.

By assuming that distortion is restricted to 𝑓𝑓 and that line voltage is pure sinusoidal, Equations 6–9 can be valid.

𝑣𝑣𝑠𝑠(𝑓𝑓) = 𝑉𝑉𝑠𝑠 𝑠𝑠𝑠𝑠𝑛𝑛 𝑛𝑛𝑓𝑓 (6)

𝑠𝑠𝑠𝑠(𝑓𝑓) = 𝑑𝑑𝑠𝑠𝑠𝑠𝑓𝑓𝑃𝑃𝑃𝑃𝑓𝑓𝑃𝑃𝑑𝑑 (𝑛𝑛𝑃𝑃𝑛𝑛 − 𝑠𝑠𝑠𝑠𝑛𝑛𝑠𝑠𝑠𝑠𝑃𝑃𝑠𝑠𝑑𝑑𝑓𝑓𝑠𝑠) (7)

The PF can now be expressed as in Equation 8.

𝑃𝑃𝑃𝑃 = 𝐼𝐼𝑠𝑠1,𝑟𝑟𝑟𝑟𝑠𝑠𝐼𝐼𝑠𝑠,𝑟𝑟𝑟𝑟𝑠𝑠

cos 𝜃𝜃1 = 𝑘𝑘𝑑𝑑𝑖𝑖𝑠𝑠𝑛𝑛𝑝𝑝𝑝𝑝𝑛𝑛𝑖𝑖𝑝𝑝𝑛𝑛 × 𝑘𝑘𝑑𝑑𝑖𝑖𝑠𝑠𝑝𝑝𝑅𝑅𝑅𝑅𝑐𝑐𝑅𝑅𝑑𝑑𝑅𝑅𝑛𝑛𝑛𝑛 (8)

The 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 (THD with respect to current) is defined by Equation 9.

𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = �∑ 𝐼𝐼𝑠𝑠𝑛𝑛,𝑝𝑝𝑑𝑑𝑠𝑠

2∞𝑛𝑛=2

𝐼𝐼𝑠𝑠1,𝑝𝑝𝑑𝑑𝑠𝑠2 = �

1𝑘𝑘𝑑𝑑𝑖𝑖𝑠𝑠𝑛𝑛𝑝𝑝𝑝𝑝𝑛𝑛𝑖𝑖𝑝𝑝𝑛𝑛

2 − 1 (9)

As seen from Equations 8 and 9, PF and THD are related to distortion and displacement factors. An im-provement in PF may, consequently, lead to reduction in harmonic content within the network.

2.2 Capacitor voltage support Applying shunt capacitors to a system results in a voltage rise caused by the flow of capacitor current (or the reduction of inductive current) through the inductive reactance of the system from the point of installation back to the generation. The voltage rise at the capacitor location is approximately equal to the capacitor current IC times the inductive reactance XL of the system. There is a voltage rise all the way back to the voltage source, the magnitude depend-ing on the inductive reactance between the source and the location. In a radial system, there is also an increase in the voltage beyond the capacitor location resulting from the increase at the capacitor location. The voltage rise that capacitors will produce based on the IC and the XL of the system to the capacitor location is given by Equation 10.

∆𝑉𝑉 = 𝐼𝐼𝐷𝐷𝑋𝑋𝐿𝐿 (10)

For systems with a reasonably high X/R ratio, where the short-circuit impedance to the capacitor

location is about the same as the inductive reac-tance, XL in Equation 10 is the impedance that de-termines the system short-circuit current available at the capacitor location. This short-circuit current is useful in estimating the voltage rise. A commonly used estimate is given by Equation 11.

∆𝑉𝑉 = 𝑉𝑉 𝐼𝐼𝐶𝐶𝐼𝐼𝑆𝑆𝐶𝐶

(11)

2.3 Increased system capacity Increased system capacity may justify the addition of shunt power capacitors on a distribution system. This is particularly significant when loads supplied by the system are increasing rapidly. The addition of shunt power capacitors reduces the volt-ampere (VA) loading on the system, thereby releasing ca-pacity that can then be used to supply future load increases. The power factor required to release the desired amount of system kVA can be determined by Equation 12.

𝑃𝑃𝑃𝑃𝑛𝑛𝑅𝑅𝑝𝑝 = 𝑃𝑃𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜1×𝑆𝑆𝑟𝑟𝑟𝑟𝑜𝑜𝑟𝑟𝑟𝑟𝑠𝑠𝑟𝑟𝑘𝑘𝑉𝑉𝐴𝐴

(12)

To calculate the capacitive kVAr (kilo volt Am-pere reactive) necessary to correct to a new, higher power factor, the inductive kVAr of the new (cor-rected) power factor is subtracted from the old (ex-isting) power factor. The difference is the amount of capacitive kVAr to be added to the system. Equation 13 is a convenient way of doing this.

𝑄𝑄𝐷𝐷 = 𝑃𝑃𝑆𝑆[tan (cos−1 𝑃𝑃𝑃𝑃𝑝𝑝𝑅𝑅𝑑𝑑) − tan (cos−1 𝑃𝑃𝑃𝑃𝑛𝑛𝑅𝑅𝑝𝑝)] (13)

2.4 Size and number of capacitor banks The shunt capacitance requirements are determined for a power system by modelling the system for var-ious contingencies and determining the capacitors required to maintain acceptable system voltage. The maximum capacitor bank size is influenced by:

• change in system voltage upon capacitor bank switching; and

• switchgear continuous current limitations When a capacitor bank is energised or de-ener-

gised, the fundamental system voltage increases or decreases, respectively. This voltage change is often limited to a value in the range of 2 - 3% to have a minimal effect upon customer loads. This voltage change (ΔV) can be estimated by Equation 14.

𝑉𝑉 = �𝑄𝑄𝐶𝐶𝑀𝑀𝑉𝑉𝐴𝐴𝑅𝑅𝑆𝑆𝑆𝑆𝐶𝐶𝑀𝑀𝑉𝑉𝐴𝐴

� × 100% (14)

where V is the voltage change as a percentage of the fundamental frequency rms system voltage; 𝑄𝑄𝐷𝐷𝑀𝑀𝑉𝑉𝑀𝑀𝑀𝑀 is the mega volt-ampere reactive (MVAR) size of the


capacitor bank; and 𝑆𝑆𝑆𝑆𝐷𝐷𝑀𝑀𝑉𝑉𝑀𝑀 is the available three-phase short-circuit mega volt-ampere (MVA).

2.5 Switching transients during energisation When a capacitor bank is energised or de-energised, current and voltage transients are produced, affect-ing both the capacitor bank and the connected sys-tem. Transient frequencies caused by isolated ca-pacitor bank switching generally fall in the range of 300–1000 Hz. The characteristic frequency is re-lated to the steady-state voltage rise (ΔV) using Equation 15.

𝑓𝑓𝑠𝑠 =1

2�𝐿𝐿𝑠𝑠𝐶𝐶= 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛𝑅𝑅𝑑𝑑 × ��

𝑆𝑆𝑆𝑆𝐷𝐷𝑀𝑀𝑉𝑉𝑀𝑀𝑄𝑄𝐷𝐷𝑀𝑀𝑉𝑉𝑀𝑀𝑀𝑀

�

= 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛𝑅𝑅𝑑𝑑 × ��1𝑉𝑉� (15)

Capacitor switches must be capable of repeatedly withstanding inrush current, which, for an isolated capacitor bank, is as given by Equations 16–19.

𝐼𝐼max𝑝𝑝𝑘𝑘 = 1000 × 𝑉𝑉𝐿𝐿𝐿𝐿 × �23

× �𝐷𝐷𝑟𝑟𝑒𝑒𝐿𝐿𝑟𝑟𝑒𝑒

(16)

= √2 × �𝐼𝐼𝑆𝑆𝐷𝐷 × 𝐼𝐼1 (17)

= 1000𝑉𝑉𝐿𝐿𝐿𝐿

× �23

× �𝑆𝑆𝑆𝑆𝐷𝐷𝑀𝑀𝑉𝑉𝑀𝑀 × 𝑄𝑄𝐷𝐷𝑀𝑀𝑉𝑉𝑀𝑀𝑀𝑀 (18)

= 1000 × �23

× �𝑄𝑄𝐶𝐶𝑘𝑘𝑉𝑉𝐴𝐴𝑅𝑅

1000×2×𝑓𝑓𝑠𝑠×𝐿𝐿𝑟𝑟𝑒𝑒 (19)

2.6 Evaluation of approaches in terms of filter types Table 1 shows the high-level differences in terms of power electronics, complexity, cost, technology, steps and size between passive, active, and hybrid filters. In this study, passive filters are selected as the most viable option because of financial constraints, however the specified solution makes use of a mul-tistep configuration thereby benefitting from similar technology improvements as with active and hybrid filters.

2.7 Problem formulation In recent years, increasing attention has been paid to minimise the energy cost and inefficiency in elec-tricity distribution system. One of the methods to minimise energy cost is to incorporate PFC in the

reticulation network. Harmonics cause the following unwanted symptoms in the power system networks [16, 19–21]:

• high levels of reactive power;

• high neutral current;

• low PF;

• voltage distortion; and

• low energy efficiency.

Harmonic filters can suppress harmonic distor-tion in any reticulation network [22–25]. A compen-sator needs to be specified for fluctuating modular plant loading conditions, which is then capable of maintaining the harmonic distortion levels well within the prescribed limits [26–29]. An economical solution is required in which the capital investment cost related to PFC is recoverable in short time be-cause of lower procurement cost of reactive power [27, 30]. The present study was based on the follow-ing main objectives [31–34]:

• to mitigate poor PF caused by inductive loads such that a near unity PF is measured on the supply distribution side;

• to control and limit the propagation of har-monics in the broader network in accordance with prescribed THD criteria to such an extent that near sinusoidal source currents are meas-ured at the distribution level; and

• to free up capacity in terms of apparent power available upstream from the installed capacitor location.

3. Load flow analysis on Grootegeluk Mine 3.1 Network configuration Figure 1 illustrates the DIgSilent PowerFactory over-all network configuration. At the time of this study, two 132/33 kV, 80 MVA transformers were in ser-vice, with a third transformer planned to be commis-sioned in 2017. These transformers are connected to a 33 kV main substation double busbar arrange-ment consisting of 33 kV main and reserve busbars that are normally operated in a split configuration. Transformer 2 is connected to the 33 kV reserve bus-bar that supplies the ‘new’ plant consisting of reduct-ants, north pit and Grootegeluk (GG) 7 and 8 sub-station ring networks. Once transformer 3 is com-missioned it will also be connected to the 33 kV re-serve busbar. Transformer 1 is connected to the 33 kV main busbar that supplies the ‘old’ plant consist-ing of GG1, GG2 and main pit substations.

Table 1: Available filter types [1, 3].

Filter type Power electronics Complexity Cost Technology Multistep Size

Passive No Low Low Outdated Yes Bulky Active Yes High High Modern Yes Smallest Hybrid Yes Medium Medium Modern Yes Smaller

38

Figure 1: The DIgsilent PowerFactory overall network configuration.

FUTURE

o Node – Open

• Node – Closed


Figure 2: DIgSilent PowerFactory main pit network configuration.

Figure 2 illustrates the DIgSilent PowerFactory main pit network configuration. The main pit net-work is supplied by both the 33/11 kV main pit sub-station and the 33/11 kV north pit substation that enable 80 MVA transformers at the 132/33 kV main substation to be operated in an open or closed con-figuration. The existing 11 kV PFC banks at main pit, GG1 and GG2 are as follows:

• GG1 and GG2: two 8 MVAR PFC single fil-ters tuned at 4.7 pu (per unit), utilising air core reactors; and

• main pit: 6 MVAR PFC damped C type filter utilizing air cored reactors, tuned at 4.7 pu.

3.2 Existing and future system load Table 2 presents the 2015 – 2017 total system load on two transformers at the 132/33 kV main substa-tion. Table 3 presents the 2015 substation load breakdown within the network model that will be considered for the switched PFC filter bank designs at north pit, GG 7 and 8 and reductants 33/11 kV substations. It is evident that the total load value of 88.74 MVA from Table 3 is supplied from trans-

former 2. Network losses are responsible for the re-duction in the total load from 90.80 MVA to 88.74 MVA. The loading on transformer 2 of 90.80 MVA exceeds its rated capacity of 80 MVA. Table 2 also presents the 2017 total system on three transformers at the 132/33 kV main substation. Table 3 also shows the 2017 substation load breakdown within the network model that will be considered for the switched PFC filter bank designs at north pit, GG 7 and 8 and reductants 33/11 kV substations. The in-troduction of transformer 3 connected to the reserve busbar alleviates the overloading conditions on transformer 2, because the respective transformers are sharing the load to the north pit and GG 7 and 8 and reductants 33/11 kV substations.

Some additional loads not represented in Tables 2 and 3 can be divided into two main areas as fol-lows.

• Grootegeluk expansion plan: The pit area will expand to the West with additional load added to north pit and main pit substations in 2017 and 2021; and

• Thabametsi Coal Plant: An additional +/-20 MVA temporary construction load for the


planned Thabametsi Coal plant. This addi-tional load is planned to be supplied from the existing 33 kV reductants, north pit and GG 7 and 8-ring networks.

This additional load is planned to be phased into

the existing system load within the next six years. These additional loads that do not form part of the

loading populated within the DIgSilent PowerFac-tory model and were excluded from the assessment and do not form part of the detailed planning of the proposed switched PFC filter banks on 11 kV at north pit, GG 7 and 8 and reductants substations. The additional load will, however, influence the overall power factor correction on 33 kV and addi-tional PFC may be required.

Table 2: The 2015–2017 system loading, PFCs at GG1, GG2 and main pit.

System load Feeder name P (MW) Q (MVAR) S (MVA) PF

Max loading condition (LV side)

Eskom Tx 1 80MVA, 33 kV 30.45–30.44 0.39–0.57 30.45–30.45 ≈1.0

Eskom Tx 2 80MVA, 33 kV 75.38–44.38 50.61–31.30 90.80–54.31 0.830–0.817

Eskom Tx 3 80MVA, 33 kV 0–44.38 0–31.30 0–54.31 0–0.817

Total (2015–2017) 105.83–119.20 51.00–63.17 121.25–139.07 0.873–0.857 PF = power factor, Tx = transformer, LV = low voltage, PF = power factor, P = real power, Q = Reactive Power, S = apparent power

Table 3: The 2015–2017 substation loading, PFCs at GG1, GG2 and main pit.


Max loading condition (HV side)

Reductants, 33 kV total 11.49–11.49 5.81–5.81 12.87–12.87 0.892–0.892

GG 7 and 8, 33 kV total 34.58–34.58 21.51–21.51 40.73–40.73 0.849–0.849

North pit, 33 kV total 28.70–41.76 20.27–30.66 35.14–51.80 0.817–0.806

Total (2015–2017) 74.77–87.83 47.59–57.98 88.74–105.40 0.844–0.835

HV = high voltage, PFC = power factor correction, GG = Grootegeluk, PF = power factor, P = real power, Q = Reactive Power, S = apparent power

3.3 Power factor correction bank sizes and system improvements The sizing of the switched PFC Filter Banks makes provision for future network expansion and ramp loading to ensure that the PFC is effective for a wide range of plant loading. The results of the different loading conditions are shown in Table 3. The PFC requirements to ensure a PF of at least 0.97 at the 33 kV north pit, GG 7 and 8 and reductants substa-tions are shown in Table 4 requiring the installation of a 2.94 MVAR bank at 11 kV reductants, a 12.85 MVAR bank at 11 kV GG 7 and 8, as well as a 13.08 MVAR (2015 loading) – 20.20 MVAR (2017 load-ing) bank at 11 kV north pit. To ensure uniform PFC equipment throughout the system for ease of con-struction and maintenance, the switched PFC banks are proposed with 1.5 MVAR step increments at spe-cific substations as shown in Table 4. Note that the total 33 kV PFC specified of 31.50 MVAR is higher than calculated requirement because of 20 MVA, 33/11 kV distribution transformer magnetisation ef-fects.

Based on the network simulations, the maximum 2015 power consumption for this study at reductants substation is 11.49 + j5.81 MVA, a 4.5 MVAR switched PFC filter bank is proposed to ensure a PF

of 0.994 at maximum substation loading. The pro-posed bank consists of two stages, 1 x 1.5 MVAR and 1 x 3.0 MVAR to be installed on busbar 1 and 2 respectively. Similarly, based on the 2015 power consumption at the GG 7 and 8 substation of 34.58 + j21.51 MVA, a 10.5 MVAR switched PFC filter bank is proposed to ensure a power factor of 0.956 at maximum substation loading. The proposed bank consists of three stages, 1 x 1.5 MVAR, 1 x 3.0 MVAR and 1 x 6.0 MVAR to be installed on busbar 1, 2 and 3 respectively.

The 2015 power consumption at the north pit substation is 28.70 + j20.27 MVA and its 2017 power consumption is 41.76 + j30.66 MVA. A 16.5 MVAR switched PFC filter bank (strategically se-lected as a value between the 2015 and 2017 load-ing condition) is proposed to ensure a PF of 0.992 at 2015 maximum substation loading. The pro-posed bank consists of four stages; a 1 x 1.5 MVAR and a 1 x 6.0 MVAR to be installed on busbar 1, and 1 x 3.0 MVAR and 1 x 6.0 MVAR to be installed on busbar 2. Table 5 summarises the results from the network assessment with the 2015 and 2017 maxi-mum power consumption at main 132/33 kV sub-station with the installation of proposed switched PFC filter banks.

41

Table 4: The 2015–2017 Substation loading, PFCs size specified (reductants, GG 7 and 8, north pit).

System load Feeder name PF PFC required PFC specified PF rectified

Max loading condition (HV side)

Reductants, 33 kV total 0.892 2.94 4.50 0.994 (lag)

GG 7 and 8, 33 kV total 0.849 12.85 10.50 0.956 (lag)

North pit, 33 kV total 0.817–0.806 13.08–20.20 16.50 0.992 (lag)

Total (2015–2017) 0.844–0.835 28.85–35.98 31.50 0.978 (lag)

HV = high voltage, PF = power factor, PFC = power factor correction, GG = Grootegeluk

Table 5: The 2015–2017 system loading with power fact correction system improvement.


Max loading condition (LV side)

Eskom Tx 1 80 MVA, 33 kV 30.45–30.44 0.30–0.49 30.46–30.46 ≈1.0

Eskom Tx 2 80 MVA, 33 kV 75.38–44.38 16.20–13.38 76.88–46.17 0.957–0.978

Eskom Tx 3 80 MVA, 33 kV 0–44.38 0–13.38 0–46.17 0–0.957

Total (2015–2017) 105.83–119.20 16.50–27.25 107.34–122.80 0.984–0.97

LV = low voltage, Tx = transformer, PF = power factor, P = real power, Q = Reactive Power…, S = apparent power

Figure 3: 2015, max system loading, 33 kV system power flow triangle

The proposed banks will ensure an overall PF of

0.97 for both the 2015 and 2017 maximum power consumption and will decrease the system power re-quirement from 119.20 + j63.17 MVA to 118.84 + j27.25 MVA.

3.4 The MVA power reduction with PFC Figure 3 shows the power triangle of the 33 kV sys-tem, based on the combined power flow from the 33 kV main intake substation to the 33 kV GG 7 and 8 networks with 16.5 MVAR, 10.5 MVAR, and 4.5 MVAR switched PFC banks installed at the 11 kV north pit, GG 7 and 8, and reductants substations respectively. Note the improvement in power factor, as well as the reduction in apparent power with switched PFC banks installed.

4. Harmonic analysis Harmonic analysis consists of both harmonic fre-quency scans and harmonic voltage distortion anal-ysis. Harmonic frequency scans would show har-monic impedance peaks relative to harmonic order. Areas of concern exist where these peaks are above the threshold of 2.5 x linear impedance and would be further investigated in terms of harmonic voltage distortion. Harmonic voltage distortion analysis pro-vides information used to determine the required harmonic filtering to comply with NRS048-2 (Na-tional energy regulator power quality standard). For the purposes of this study, only the results of 11 kV north pit substation are presented.

PF = 0.86

6 3.17 M VAR (Without PFC)

1 19.20 M W 3 1. 50 M VAR (PFC banks)

1 39.07 M VA

PF =0.97

2 7.25 M VAR (With PFC) 1 22.80 MVA

0 M VAR (New Excess)


4.1 Harmonic frequency scan The DIgSilent PowerFactory model was used to sim-ulate the 11 kV harmonic impedances, which is pre-sented in this paper. The following harmonic fre-quency labelling, as indicated in the frequency scan charts and tables, was used:

• Existing network: The 11 kV network harmonic impedance with the existing 11 kV harmonic fil-ter banks at Main Pit, GG1 and GG2 in service. The existing harmonic filters consist of: o GG1 and GG2: Two 8 MVAR PFC single fil-

ters tuned at 4.7 pu, utilising air core reactors; and

o Main pit: Six MVAR PFC damped C-type fil-ter, utilising air cored reactors tuned at 4.7 pu.

• Plain PFC banks: The 11 kV network harmonic impedance with the existing 11 kV harmonic fil-ter banks in service at the Main Pit, GG1 and GG2 and with plain PFC switched banks at the 11 kV GG 7 and 8 (10.5 MVAR), North Pit (16.5 MVAR) and Reductants (4.5 MVAR) substations, respectively.

• PFC filter banks 4.7 tuned: The 11 kV network harmonic impedance with the existing 11 kV har-monic filter banks in service at the main pit, GG1 and GG2 and with fifth harmonic filter switched banks at the 11 kV GG7 and 8 (10.5 MVAR), north pit (16.5 MVAR) and reductants (4.5 MVAR) substations, respectively.

The frequency scans were performed at 50% loading to represent the load damping effect at the parallel resonant peaks. The simulated harmonic im-pedances more than the 2.5 x linear impedance were flagged. These harmonic impedances and har-monic voltage distortions were further investigated in Section 4.2. In Figures 4-9 and Table 6, ‘Base’ represents the frequency scans with the 11 kV power system configured with the 11 kV feeders that con-nect the main pit and north pit substations operating N/O at the main pit substation. The pit area is sup-plied from the north pit substation. In the graphs that follow, the solid line represents the linear impedance calculated by Equation 20.

Z(𝑛𝑛) = n𝑍𝑍50𝐻𝐻𝐻𝐻 (20)

where 𝑍𝑍50𝐻𝐻𝐻𝐻 represents the system impedance at 50 Hz, as calculated from the symmetrical short-circuit level.

Furthermore, the vertical axis on all the graphs that follow represents the harmonic impedance at 50% loading and the horizontal axis on all the graphs represents the harmonic order. The upper harmonic impedance threshold is defined as the 2.5 x linear impedance. The 11 kV network and PFC configurations that result in parallel resonant peaks

above the upper harmonic threshold can result in voltage harmonic distortions above the NRS048 harmonic distortion planning levels and must be in-vestigated in detail. A high linear impedance Z(𝑛𝑛) can result in individual voltage harmonic dis-tortions 𝑉𝑉𝑛𝑛 , according to Ohm’s law in Equation 21.

𝑉𝑉𝑛𝑛 = 𝑍𝑍𝑛𝑛 × 𝐼𝐼𝑛𝑛 (21)

If the voltage harmonic is above the NRS048 planning levels, harmonic filtering or different types or combinations of harmonic filters should be con-sidered. The voltage harmonic distortions associated with the frequency scans are evaluated in Section 4.2. Figure 4 shows the results of a frequency scan performed on the 11 kV north pit busbar 1 with the existing 11 kV PFC banks in service at main pit, GG1 and GG2. The results indicate dominant par-allel resonant peaks around the twenty-first and twenty-third harmonic orders, well above the 2.5 x linear impedance. Although the twenty-second har-monic impedance is high, it is not a concern, as it does not coincide with the characteristic harmonics.

Figure 5 shows the result of a frequency scan per-formed on the 11 kV north pit busbar 1 with the ex-isting 11 kV PFC banks in service at main pit, GG1 and GG2 and with 16.5 MVAR, 10.5 MVAR and 4.5 MVAR switched plain PFC banks installed in the 11 kV north pit, GG7 and 8 and reductants substations, respectively. Additionally, the graph indicates the change in harmonic impedance as the step-size of the 16.5 MVAR plain-PFC bank at the north pit sub-station is varied.

Figure 5 also indicates that, for each PFC config-uration, two parallel resonant peaks exist per config-uration. One peak is characterised as a severe par-allel resonant peak of high harmonic order well above the 2.5 x linear impedance. The other peak is a less severe peak of a lower harmonic order, cen-tred near the fourth harmonic order. From the graph, it can also be noted that, as the size of the 16.5 MVAR plain PFC bank at the north pit substa-tion increases (due to step variation), the severe peaks shift in order from the fifteenth to the seventh and the impedance magnitude decreases. However, there is a tight grouping of peaks near the fourth har-monic order that stays relatively constant in both or-der and magnitude as the PFC step size is varied. Figure 6 shows the result of a frequency scan per-formed on the 11 kV north pit busbar 1 with the ex-isting 11 kV PFC banks in service at main pit, GG1 and GG2 and with 16.5 MVAR, 10.5 MVAR and 4.5 MVAR switched PFC banks (tuned with fifth har-monic LC filters) installed in the 11 kV north pit, GG7 and 8 and reductants substations, respectively. Additionally, the graph indicates the change in har-monic impedance as the step size of the 16.5 MVAR plain PFC bank at the north pit substation is varied.


Figure 6 also indicates the change in the har-monic impedance response with the fifth harmonic LC filters in service. The severe parallel resonant peaks that are well above the 2.5 x linear impedance line are still present and have shifted from the fif-teenth harmonic order to the twenty-fourth har-monic order. The less severe peaks that were present at the fifth harmonic order have been eliminated by the LC filters with peaks still present at the third har-monic order. A parallel resonant peak at the twenty-

first harmonic order is present in the existing net-work. With a plain switched filter bank, there is a parallel resonant peak with a smaller magnitude at the fifth and seventh harmonic orders. For the switched PFC devices, harmonics from the fifth or-der to the twenty-third order are eliminated by the installation of the PFC tuned with fifth harmonic LC filters. There are still third order harmonics present on these networks that are above the 2.5 x linear impedance and their effects on the harmonic voltage distortion are assessed in Section 4.2.

Figure 4. North pit sub, frequency scan, 11 kV busbar (existing network),

where NP = north pit.

Figure 5. North pit substation, frequency scan (PFC banks), where PFC = power

factor correction and NP = north pit.

0

10

20

30

40

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19 21 23 25

Harm

onic

Impe

danc

e@

50%

Load

ing

(Ohm

)

Harmonic Order (p.u.)

Linear 2.5 Times NP_NP MP Close_Existing Network NP_NP MP Open_Existing Network

0

20

40

60

80

100

120

140

160

180

1 3 5 7 9 11 13 15 17 19 21 23 25

Harm

onic

Impe

danc

e@

50%

Load

ing

(Ohm

)


Linear 2.5 Times NP_NP MP Open_PFC_00 NP_NP MP Open_PFC_15 NP_NP MP Open_PFC_30

NP_NP MP Open_PFC_45 NP_NP MP Open_PFC_60 NP_NP MP Open_PFC_75 NP_NP MP Open_PFC_90 NP_NP MP Open_PFC_105

NP_NP MP Open_PFC_120 NP_NP MP Open_PFC_135 NP_NP MP Open_PFC_150 NP_NP MP Open_PFC_165


Figure 6: North pit sub, frequency scan, 11 kV busbar (power factor corrections

filter banks tuned at 4.7 pu; step).

Table 6: Six-pulse rectifier characteristic harmonic current content.

Harmonic order Harmonic current content (%)

Harmonic order Harmonic current content (%)

3 1.0 15 1.0

5 17.5 17 0.5

7 11.0 19 0.2

9 1.0 21 0.1

11 4.5 23 0.1

13 2.9 25 0.1

4.2 Harmonic voltage distortion The harmonic voltage distortion within the 33/11 kV power system was simulated based on the assump-tion that 15% of the connected load base will be nonlinear to simulate the unknown harmonic cur-rent content of the future plant. This was achieved by inserting characteristic six-pulse rectifier har-monic lumped loads onto the 11 kV north pit bus-bars, while scaling the normal loads to 35% of the 2017 loading values. The harmonic distortion was chosen to simulate a voltage THD of approximately 4.2% on the existing 11 kV north pit busbar with no PFC installed. The lumped loads have a harmonic current content at specific harmonic orders, as shown in Table 6.

Figure 7 evaluates the expected voltage har-monic distortion due to the high twenty-first har-monic impedance, as shown in Figure 4. It also shows the result of a harmonic load flow performed on the 11 kV north pit busbar 1 with the existing 11 kV PFC banks in service at main pit, GG1 and GG2.

Figure 7 shows that, with only the existing PFC devices in service at the GG1, GG2 and main pit substations, the 11 kV voltage harmonic content of the fifteenth harmonic at the north pit substation is above the NRS048-4 planning criteria (acceptable distortion levels).

Figure 8 evaluates the expected voltage har-monic distortion in accordance to the harmonic fre-quency scan shown in Figure 5. It also shows the result of a harmonic voltage distortion analysis per-formed on the 11 kV north pit busbar 1 with the ex-isting 11 kV PFC banks in service at main pit, GG1 and GG2 and with 16.5 MVAR, 10.5 MVAR and 4.5 MVAR switched plain PFC banks installed in the 11 kV north pit, GG7 and 8 and reductants substa-tions, respectively. Further, it indicates the change in harmonic voltage distortion during the switching contingencies of the 16.5 MVAR plain PFC bank at the north pit substation.

0

20

40

60

80

100

120

1 3 5 7 9 11 13 15 17 19 21 23 25

Harm

onic

Impe

danc

e@

50%

Load

ing

(Ohm

)


Linear 2.5 Times NP_NP MP Open_PFC 47_00 NP_NP MP Open_PFC 47_15 NP_NP MP Open_PFC 47_30

NP_NP MP Open_PFC 47_45 NP_NP MP Open_PFC 47_60 NP_NP MP Open_PFC 47_75 NP_NP MP Open_PFC 47_90 NP_NP MP Open_PFC 47_105

NP_NP MP Open_PFC 47_120 NP_NP MP Open_PFC 47_135 NP_NP MP Open_PFC 47_150 NP_NP MP Open_PFC 47_165

45

Figure 7: North pit sub, voltage distortion, 11 kV busbar (existing network).

Figure 8: North pit sub, voltage distortion, 11 kV busbar (plain PFC banks; step).

In Figure 8 with the existing PFC in service on 11

kV GG1, GG2 and main pit as well as the plain PFC at the GG7 and 8 networks, the fifth and seventh voltage harmonics are well above the NRS048 lev-els. The THD is also well above the NRS048 com-patibility levels for the 11 kV and 33 kV busbars. The high fifth and seventh impacting the THD values, when using a plain PFC bank, are a concern. With the fifth harmonic current dominant in most parts of the plant, it is recommended that a harmonic filter solution, tuned close to the fifth harmonic should be implemented. Figure 9 evaluates the expected volt-age harmonic distortion in accordance to the har-monic frequency scan shown in Figure 6. In Figure 9 the introduction of fifth harmonic filters on the 11

kV north pit, GG7 and 8 and reductants substations (existing PFC simulated on GG1, GG2 and main pit) dramatically reduces the voltage harmonic con-tent on both the 11 kV and 33 kV networks.

The voltage harmonic content at the north pit substation is now well within the NRS048 planning limits. The fifth harmonic LC filters are therefore ef-fective, reducing the voltage harmonic distortion lev-els to below the NRS048 planning limits, and will prevent negative impacts on the utility voltage. The reduction in the individual voltage harmonics is clearly visible when compared to the scenarios where plain PFC were installed on the 11 kV net-work shown in Figure 8.

0

2

4

6

8

10

12

14

16

THD 3 5 7 9 11 13 15 17 19 21 23 25

Volta

ge H

arm

onic

Dis

tort

ion

(%)

Harmonic Order

NRS048 Planning NP_NP MP Open_PFC_00 NP_NP MP Open_PFC_15 NP_NP MP Open_PFC_30 NP_NP MP Open_PFC_45

NP_NP MP Open_PFC_60 NP_NP MP Open_PFC_75 NP_NP MP Open_PFC_90 NP_NP MP Open_PFC_105 NP_NP MP Open_PFC_120

NP_NP MP Open_PFC_135 NP_NP MP Open_PFC_150 NP_NP MP Open_PFC_165

0

1

2

3

4

5

6

7

THD 3 5 7 9 11 13 15 17 19 21 23 25

Volta

ge H

arm

onic

Dist

ortio

n (%

)

Harmonic Order

NRS048 Planning NP_NP MP Close_Existing Network NP_NP MP Open_Existing Network

46

Figure 9: North pit sub, voltage distortion, 11 kV busbar

(PFC filter banks @ 4.7 tuning order; step).

The voltage harmonic content at the north pit

substation is now well within the NRS048 planning limits. The fifth harmonic LC filters are therefore ef-fective, reducing the voltage harmonic distortion lev-els to below the NRS048 planning limits, and will prevent negative impacts on the utility voltage. The reduction in the individual voltage harmonics is clearly visible when compared to the scenarios where plain PFC were installed on the 11 kV net-work shown in Figure 8.

4.3 Results and discussion Based on the load flow results obtained from the provided DIgSilent PowerFactory model, a total re-active power requirement for switched PFC banks of 31.5 MVAR was identified to ensure a 0.97 lagging PF for the 2017 system load of 119.21 + j63.17 MVA. The sizing of the switched PFC filter banks makes provision for future network expansions and ramp loading to ensure that the PFC is effective for a wide range of plant loading. It is proposed that the switched PFC filter banks tuned with 4.7 harmonic LC filters should be installed as follows: • At the north pit substation, a 16.5 MVAR

switched PFC filter bank is proposed to ensure a PF of 0.992 at the maximum substation load-ing. The proposed bank consists of four stages: 1 x 1.5 MVAR and 1 x 6.0 MVAR to be installed on busbar 1 and 1 x 3.0 MVAR and 1 x 6.0 MVAR to be installed on busbar 2.

• At the GG7 and 8 substations, a 10.5 MVAR switched PFC filter bank is proposed to ensure a PF of 0.956 at the maximum substation load-ing. The proposed bank consists of three stages:

1 x 1.5 MVAR, 1 x 3.0 MVAR and 1 x 6.0 MVAR to be installed on busbars 1, 2 and 3, respec-tively.

• At the reductants substation, a 4.5 MVAR switched PFC filter bank is proposed to ensure a PF of 0.994 at the maximum substation load-ing. The proposed bank consists of two stages: 1 x 1.5 MVAR and 1 x 3.0 MVAR to be installed on busbars 1 and 2, respectively.

5. Conclusions This research consisted of a study of power factor correction (PFC), load requirements, load flow, fault analyses, harmonic frequency scans and harmonic voltage distortion analyses. The DIgSilent Power-Factory was used to carry out investigations.

The introduction of plain PFCs on the substa-tions resulted in severe parallel resonant peaks that were well above the 2.5 x linear impedance guide-line and thus resulted in very high voltage harmonic distortions more than the NRS048-2 compatibility levels. However, the installation of switched PFC fil-ter banks tuned with fifth harmonic order resulted in a viable solution. The introduction of the switched PFC banks tuned with fifth order resonant circuit harmonic filters decreased the harmonic impedance peaks, consequently reducing the harmonic voltage distortion effects below the NRS048-2 compatibility levels. Therefore, switched PFC filter banks tuned with fifth harmonic order are the preferred solution. The installation of switched PFC filter banks tuned at the fifth harmonic order resulted in a viable solu-tion with no harmonic voltage distortion violations present in the system. The systems overall power

0

1

2

3

4

5

6

7

THD 3 5 7 9 11 13 15 17 19 21 23 25

Volta

ge H

arm

onic

Dis

tort

ion

(%)

Harmonic Order

NRS048 Planning NP_NP MP Open_PFC 47_00 NP_NP MP Open_PFC 47_15 NP_NP MP Open_PFC 47_30



NP_NP MP Open_PFC 47_165


factor was improved to above 0.96 thereby lowering energy cost, hence the proposed solution will max-imise savings achievable on the ESKOM electricity bill. Future work to further investigation includes the following.

• A proper economic evaluation should be com-pleted with the aim of confirming the most eco-nomical solution in which the capital investment cost related to PFC is recoverable in the short term because of the lower procurement costs of reactive power.

• A detailed equipment schedule aligned and tai-lored for harsh coal mining environments is needed.

• A PFC design report needs to be compiled and should include all the input data, specify the de-sign parameters, provide single line diagram of the compensator required and specify the equipment ratings.

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